document.write( "Question 917720: Solve for x and y if 2/x - 3/y = 2 and 4/x + 9/y + 1 = 0 \n" ); document.write( "

Algebra.Com's Answer #556785 by KMST(5328) $\"\"$ $\"About$

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$\"system%282%2Fx+-+3%2Fy+=+2+%2C+4%2Fx+%2B+9%2Fy+%2B+1+=+0%29\"$
\n" ); document.write( "With the \"change of variable\" $\"a=1%2Fx\"$ and $\"b=1%2Fy\"$ ,
\n" ); document.write( "the system of equations turns into
\n" ); document.write( " $\"system%282a-3b=2%2C4a%2B9b%2B1=0%29\"$ <--> $\"system%282a-3b=2%2C4a%2B9b=-1%29\"$ .
\n" ); document.write( "Multiplying the first equation times (-2) we get
\n" ); document.write( " $\"-4a%2B6b=-4\"$ ,
\n" ); document.write( "and adding that to the second equation, we get
\n" ); document.write( " $\"15b=-5\"$ --> $\"b=-5%2F15\"$ --> $\"b=-1%2F3\"$ .
\n" ); document.write( "Substituting that value into $\"2a-3b=2\"$ we get
\n" ); document.write( " $\"2a-3%28-1%2F3%29=2\"$ --> $\"2a%2B1=2\"$ --> $\"2a=2-1\"$ --> $\"2a=1\"$ --> $\"a=1%2F2\"$ .
\n" ); document.write( "going back to the original variables:
\n" ); document.write( " $\"1%2Fx=1%2F2\"$ --> $\"x=2\"$
\n" ); document.write( " $\"1%2Fy=-1%2F3\"$ --> $\"y=-3\"$ \n" ); document.write( "

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